In the applied sciences, various fields of study require the analysis of two-dimensional or three-dimensional volume data-sets wherein each data-set may have multiple attributes representing different physical properties. An attribute, sometimes referred to as a data value, represents a particular physical property of an object within a defined two-dimensional or three-dimensional space. A data value may, for instance, be an 8-byte data word which includes 256 possible values. The location of an attribute is represented by (x, y, data value) or (x, y, z, data value). If the attribute represents pressure at a particular location, then the attribute location may be expressed as (x, y, z, pressure).
In the medical field, a computerized axial topography (CAT) scanner or magnetic resonance imaging (MRI) device is used to produce a picture or diagnostic image of some specific area of a person's body, typically representing the coordinate and a determined attribute. Normally, each attribute within a predetermined location must be imaged separate and apart from another attribute. For example, one attribute representing temperature at a predetermined location is typically imaged separate from another attribute representing pressure at the same location. Thus, the diagnosis of a particular condition based upon these attributes is limited by the ability to display a single attribute at a predetermined location.
In the field of earth sciences, seismic sounding is used for exploring the subterranean geology of an earth formation. An underground explosion excites seismic waves, similar to low-frequency sound waves that travel below the surface of the earth and are detected by seismographs. The seismographs record the amplitude of seismic waves, both direct and reflected, at a given location for a given time period. Knowing the time and place of the explosion, the time of travel of the waves through the interior can be calculated and used to measure the velocity of the waves in the interior. A similar technique can be used for offshore oil and gas exploration. In offshore exploration, a ship tows a sound source and underwater hydrophones. Low frequency, (e.g., 50 Hz) sound waves are generated by, for example, a pneumatic device that works like a balloon burst. The sounds bounce off rock layers below the sea floor and are picked up by the hydrophones. In either application, subsurface sedimentary structures that trap oil, such as faults and domes are mapped by the reflective waves.
The use of seismic data to analyze subsurface geological structures, such as faults or other stratigraphic features, is relevant to interpreters searching for subsurface mineral and hydrocarbon deposits. Seismic-data traces are the record of the reflection of sonic waves from underground. These traces can be denoted as A(x, y, t), the reflection amplitude of time t at surface location (x, y). A wiggle display is a basic graphic representation for seismic applications, which may be displayed as a two-dimensional or a three-dimensional image. On a two-dimensional image, the wiggle display of seismic-data traces is commonly imaged by computing the graphics coordinate (u, v) of each amplitude and drawing polylines connecting these coordinates for each trace. The area of the amplitude above and/or below a given reference amplitude value for a given wiggle can be filled with colors to enhance the wiggle display for interpretation purposes and therefore, make faults and other stratigraphic features revealed by the wiggle display easier to recognize as generally described in U.S. Pat. No. 7,013,218, which is incorporated herein by reference. The colors for amplitude above and below the reference value are normally called positive fill and negative fill, respectively. The color fill is most commonly done by (1) drawing horizontal lines in a given color from the position determined by the reference value to the position determined by the amplitude at a given time/depth, or (2) by filling polygons formed by the reference line and amplitudes. FIGS. 4 through 6 illustrate different images produced by a commercial-software package, which uses the first approach to generate two-dimensional images of seismic-data.
FIG. 4 is an image of a variable density display. In this figure, the seismic data is collected and processed to produce three-dimensional volume data-sets comprising “voxels” or volume elements, whereby each voxel may be identified by the x, y, z coordinates of one of its eight corners or its center. Each voxel also represents a numeric data value (attribute) associated with some measured or calculated physical property at a particular location. Examples of geological seismic data values include amplitude, phase, frequency, and semblance. Different data values are stored in different three-dimensional volume data-sets, wherein each three-dimensional volume data-set represents a different data value. When multitude data-sets are used, the data value for each of the data-sets may represent a different physical parameter or attribute for the same geographic space. By way of example, a plurality of data-sets could include a seismic volume, a temperature volume and a water-saturation volume. The voxels in the seismic volume can be expressed in the form (x, y, z, seismic amplitude). The voxels in the temperature volume can be expressed in the form (x, y, z, ° C.). The voxels in the water-saturation volume can be expressed in the form (x, y, z, % saturation). The physical or geographic space defined by the voxels in each of these volumes is the same. However, for any specific spatial location (xo, yo, zo), the seismic amplitude would be contained in the seismic volume, the temperature in the temperature volume and the water-saturation in the water-saturation volume. In order to analyze certain sub-surface geological structures, sometimes referred to as “features” or “events,” information from different three-dimensional volume data-sets may be separately imaged in order to analyze the feature or event.
FIG. 5 is an image of a seismic “wiggle” display. And, FIG. 6 is a combined image of FIG. 5 (wiggle display) and FIG. 4 (voxel display). The relationship between a typical wiggle or seismic-data trace and a plurality of voxels is described more fully in U.S. Pat. No. 6,690,820 assigned to Landmark Graphics Corporation, which is incorporated herein by reference. In FIG. 5, the seismic wiggles are displayed with positive fill and negative fill.
The color fill according to the first approach (drawing horizontal lines) is faster than the second approach (filling polygons), but the first approach is not applicable in three-dimensional displays. Both approaches are normally carried out using a computer's CPU, which may be limited by the number of registers. This limitation is an important bottleneck through which a large number of seismic amplitudes (waveforms) must pass through to be visualized. At present, the current state-of-the-art seismic waveform visualization techniques using two-dimensional graphics primitives (polylines, lines, filled polygons) are insufficient to produce images of a three-dimensional volume of seismic-data traces in real-time at interactive rates-meaning at least ten (10) frames per second.
Graphical displays, however, have been generally improved by using a graphics accelerator or a graphics card to process and display other types of graphical data. For example, U.S. Patent Application Publication No. 2005-0237334-A1 assigned to Landmark Graphics Corporation, which is incorporated herein by reference, uses a graphics card to render voxel data in real-time. And, U.S. Pat. No. 7,076,735, also assigned to Landmark Graphics Corporation, uses a graphics card to render graphical data representing a three-dimensional model. Nevertheless, conventional visualization techniques, as thus described, are not capable of rendering a three-dimensional volume of seismic-data traces in real-time for contemporaneous use and analysis.